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We develop a new approach for UA, where instead of learning the spread out embeddings, users construct the embeddings with high expected minimum separability. We propose to use random binary vectors, with the length of the vectors being determined by the server such that the minimum distance between embeddings is more than a pre-determined value with high probability.
Each user then trains the model to maximize the correlation of the model outputs with their embedding vector. After training, a test input is accepted if the distance of the predicted embedding to the reference one is less than a threshold, and otherwise rejected. We develop a “warm-up phase" to determine the threshold independently for each user, in which a set of inputs are collected and then the threshold is computed so as to obtain a desired True Positive Rate (TPR).

We show our framework is privacy-preserving and addresses the security problems of existing approaches where embeddings are shared with other users or the server [1]}. Moreover, we show that using random binary embeddings enables training the UA models with significantly smaller output size than the number of users, and also allows new users to be added to training after training started without the need to change the output layer.
Finally, our method has the advantage that no extra coordination is needed among users or between the users and the server apart from the communications done usually in the FL setting.

We present experimental results of our method on VoxCeleb dataset [2]} for speaker verification. We train the models with the speech data of a subset of users (658 out of \(1,251\)  users) and evaluate the authentication performance on the data of the rest of users.
We show the models trained in the federated setting achieve high TPR at very low False Positive Rates (FPR) with different lengths of embedding vectors, \(n_e\) . For example, with a TPR of \(80\%\) , we obtained FPRs of \(0.27\%, 0.18\%\)  and \(0.16\%\)  on data of new users for \(n_e=128, 256\)  and 512, respectively.

